Chapter I: Introduction

1.  Generalities - Information is physical, revolution in quantum
mechanics, teleportation, cryptography, quantum computing
2.  Entanglement - what is it, how do we quantify it, significance in
quantum computing, notion of information being stored in correlations
rather than single particle polarizations, monogamy of entanglement
3.  Quantum measurement - Van Neumann formulation (PVMs), density matrix
formulation of QM, measuring quantum
information, other kinds of measurements (POVMs), entangling measurements, correlation measurements
4.  Quantum State estimation - previous work, main techniques, state
comparison, fidelity, purity, entropy
5.  Quasi-probability distributions - Wigner, P and Husimi
distributions, distributions on spheres, brief discussion of discrete
Wigner functions
5.  Intro to the rest of the paper

Chapter II: Experimental quantum state characterization
1.  Properties of photons that make them useful for quantum
information research, the photon as a qubit, contradiction between the
qubit picture and the bosonic picture
2.  Polarimetry/Ellipsometry of polarization states, the Poincare
sphere/Bloch sphere formulation, SU(2) symmetry
3.  Bell's inequality violation, visibility, two-polarization quantum
state tomography 
4.  Entangled photon sources - Quick review of possibilities -
Clauser, Aspect, cQED, quantum dots.  SPDC, type-I, type-II
phasematching, relationship between phase-matching and entanglement,
causes of reduced entanglement, experimental data
5.  Entangling measurements - the HOM effect, interpreting HOM effect as an
entangling measurement, the HOM as a bosonic effect, limits to two-photon visibility, dealing with
limited visibility in data analysis.  Experimental data.
6.  Summary

Chapter III: Quantum state estimation in the presence of hidden information
1.  Intro - absence of quantum statistics from quantum information,
two-mode systems examples, importance in metrology, lithography.
Schwinger model of coupled oscillators, angular momentum
representation.
2.  Quasi-probability distributions for angular momentum.  Wigner
distribution, spin-squeezing, the NOON state as the limit of
spin-squeezing, relationship between entanglement and squeezing,
information in correlations rather than in polarization
3.  Experimental issues - breakdown of the Schwinger model in the
presence of hidden information, size of the Hilbert space
4.  Quantum state tomography - Kulik and Chekhova, accounting for
hidden modes.  
5.  Two photon systems - distinction between experimental
indistinguishability and fundamental indistinguishability, reflection
in the formalism: permutation symmetric operators versus permutation
symmetric states, tracing over hidden information, interpreting
the missing density matrix elements, distinction between
distinguishabiltiy and decoherence, completeness and the significance
of distinguishability to measurements 
6.  More than two photons - relationship between permutation and
angular momentum, the permutation group, the Schur-Weyl duality,
construction of ordering-blind operators using the Schur-Weyl duality,
counting ordering-blind operators using Schur-Weyl duality, structure
of the visible density matrix, interpretation as bound on distinguishability
7.  State tomography with 3-photons - Actual measurements, retrieval
of the visible density matrix from measurements, reconstruction using
convex optimization
8.  Connecting measured density matrices to Wigner functions, errors
introduced in truncating the Hilbert space, measuring entanglement,
negativity etc. from a visible density matrix, operational
interpretation of entanglement
9.  Summary, conclusions

Chapter IV: Improving quantum state estimation using mutually unbiased bases
1. Intro - freedom of selecting different PVMs for tomography,
original choice of James et al and limitations of this choice,
balanced tomography using all the stokes parameters, bias towards
separable states, the convergence
of a tomography procedure towards the true state with scaling,
considerations regarding measurement optimality, discussion for the
maximally mixed state
2. Mutually unbiased bases: definition, Wootters proof of optimality
for state estimation, construction of MUBs for two qubits, comparison
of measurement bases, doing
entangling measurements, modeling effects of limited visibility,
experimental data, which states are best measured?
3. Discrete Wigner functions - properties of ordinary Wigner
functions, translational covariance, discrete state space, connection
to MUBs, inversion from MUBs measurements, ontological implications
4. Summary/Conclusions

Chapter V:  Measuring figures of merit without doing complete state tomography
1.  Intro: The importance of figures of merit in describing states,
purity, scaling problems of quantum state tomgoraphy 
2.  The Brun Solution: Demonstrate how multiqubit measurements can do
polynomial functions, scaling of the measurement, intuitive understanding for
purity and the singlet state, 
3.  Experimental tecnhiques: measuring the singlet state projection,
dealing with limited visibility, making impure quantum states -
Kwiat's method, liquid crystal methods, 
4.  Results, other considerations: measurement results,
comparison, HOM is more and less than a singlet state filter,
correlated noise and the purity measurement
5.  Summary/discussion

Chapter VI:  Three-party Quantum Key Distribution with Two-party
entanglement
-Probably won't include this chapter

Conclusions:
1.  Summary of major results:  
2. Future outlook - debate concerning the importance of NOON states in
tomography, indistinguishabiltiy as a gate operation in optical
lattices, 
3.  Conclusions
